{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JJUY45VRA4SRMD3IBF7ZSWLGNC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"32d4f429c011d57800aa315bbb9c43ea973c1bfd5731e49ba75e6abd78b471d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-22T15:45:09Z","title_canon_sha256":"4c1b6e3a1569291f508d8be9cf4380f0e8b45420a8f5c330fc2b6b9c6799dc22"},"schema_version":"1.0","source":{"id":"1402.5519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5519","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5519v1","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5519","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"JJUY45VRA4SR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JJUY45VRA4SRMD3I","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JJUY45VR","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:fec499eb689d1a237a6eac670a816e05b01eedc2ab40a66b997c61c5d795b85d","target":"graph","created_at":"2026-05-18T02:29:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider a macroscopic model describing a system of self-gravitating particles. We study the existence and uniqueness of non-negative stationary solutions and allude the differences to results obtained from classical gravitational models. The problem is considered on a bounded domain up to three space dimension, subject to Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Finally, we show numerical simulations that affirm our findings.","authors_text":"Oliver Tse, Ren\\'e Pinnau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-22T15:45:09Z","title":"On the Effects of Bohm's Potential on a Stationary Macroscopic System of Self-Interacting Particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5519","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:15406a9e05aba42bf541e87e56853def03e47152d4f7d3da150112e61013b2f2","target":"record","created_at":"2026-05-18T02:29:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"32d4f429c011d57800aa315bbb9c43ea973c1bfd5731e49ba75e6abd78b471d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-22T15:45:09Z","title_canon_sha256":"4c1b6e3a1569291f508d8be9cf4380f0e8b45420a8f5c330fc2b6b9c6799dc22"},"schema_version":"1.0","source":{"id":"1402.5519","kind":"arxiv","version":1}},"canonical_sha256":"4a698e76b10725160f68097f9959666899f2cd8d1dd1d435e728df06faaebf29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a698e76b10725160f68097f9959666899f2cd8d1dd1d435e728df06faaebf29","first_computed_at":"2026-05-18T02:29:55.115518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:55.115518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PsoQf7D1Sx7KNVYJn6h8ohBH5GU9UoUnav4vF+HIcrbISNXNyeGZIElczH/BeEWpsZGAOvqypERLzJaHbPXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:55.115934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15406a9e05aba42bf541e87e56853def03e47152d4f7d3da150112e61013b2f2","sha256:fec499eb689d1a237a6eac670a816e05b01eedc2ab40a66b997c61c5d795b85d"],"state_sha256":"749a4a66d0c446cc9f919119be58f7b3be6d18815194225b0a523ee0cc869206"}